Test 1

Which of the following is not a property of​ inequalities?

For c less than 0c<0​, if a less than ba<b​, a minus c greater than b minus ca−c>b−c.

Which of the following statements is not ​true?

Given an ordered pair of the form​ (x,y), y is called the coordinate.

Which of the following is typically not one of the three ways to describe the solutions to a linear​ inequality?

Write the solution in inequality form.

Which of the following equations is not a disguised quadratic​ equation?

x5−x3−6=0

If u is an algebraic expression and c is a real number such that c greater than 0c>0​, then the inequality StartAbsoluteValue u EndAbsoluteValue less than cu<c is equivalent to

negative c less than u less than c−c<u<c. .

Which of the following is a rational​ equation?

6 x−1= 4 x−2

Which of the following statements is​ true?

All linear equations and all quadratic equations are polynomial equations.

Which of the following statements best defines the term​ "extraneous solution"?

An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.

Given two points which represent the endpoints of the diameter of a​ circle, which of the following statements is​ true?

The center of the circle is the midpoint of the given endpoints of the diameter.

Which of the following statements is true about linear equations of the form ax plus b equals 0 question mark ax+b=0?

The constants a and b must be real numbers with the constant a never equal to zero.

Which of the following statements describes the absolute value of a number a​?

The distance from the number a to 0 on a number line can be represented by the absolute value of a number a.

Which statement describes how to derive the equation of a circle in standard​ form?

The equation of a circle can be derived using the distance formula.

Which of the following statements is true about the equation y equals by=b​?

The equation y equals by=b is the equation of a horizontal line with zero slope.

Which of the following statements best describes how to derive the quadratic​ formula?

The quadratic formula can be derived by solving the equation ax squared plus bx plus c equals 0ax2+bx+c=0​, a not equals 0a≠0​, for x using the method of completing the square.

Which of the following statements is not​ true?

The solutions to quadratic equations are always real numbers.

Given that the points left parenthesis x 1 comma y 1 right parenthesisx1,y1 and left parenthesis x 2 comma y 2 right parenthesisx2,y2 are endpoints of a line​ segment, which of the following statements is​ true?

The x​-coordinate of the midpoint of the line segment can be found by first taking the sum of x 2x2 and x 1x1 and then dividing the sum by two.

Suppose that you are solving a quadratic equation and realize that the discriminant is equal to 7. Which of the following statements best describes the solutions to this quadratic​ equation?

There must be two real solutions.

Which of the following statements is not true concerning the equation x squared minus c equals 0 for c greater than 0 question mark x2−c=0 for c>0?

This equation is not considered to be a quadratic equation because it is not of the form ax squared plus bx plus c equals 0ax2+bx+c=0.

If u is an algebraic expression and c is a real number such that c greater than 0c>0​, then the equation StartAbsoluteValue u EndAbsoluteValue equals cu=c is equivalent to

u equals negative cu=−c or u equals cu=c.

If u is an algebraic expression and c is a real number such that c greater than 0c>0​, then the inequality StartAbsoluteValue u EndAbsoluteValue greater than cu>c is equivalent to

u less than minus cu<−c or u greater than cu>c.

Which of the following equations is in​ point-slope form?

y−y1=mx−x1

Which of the following does not describe the​ slope, m, of a nonvertical line passing through the points left parenthesis x 1 comma y 1 right parenthesisx1,y1 and left parenthesis x 2 comma y 2 right parenthesisx2,y2​?

m= x2−x1 y2−y1

Given the equation of a line in standard​ form, Ax plus By equals Upper CAx+By=C with Bnot equals≠​0, which of the following represents the slope of this​ line?

m=− A B

Which of the following is not a valid strategy when solving a polynomial equation of the form ax cubed plus bx squared equals cx question mark ax3+bx2=cx?

Divide the equation by x.

Which of the following statements is not ​true?

Given any two distinct lines in the Cartesian​ plane, the two lines will either be parallel or perpendicular.

Which of the following best describes the zero product​ property?

If two factors multiplied together are equal to​ zero, then at least one of the factors must be zero.

Which of the following statements is true about rational​ equations?

It is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions.

Which of the following statements is​ true?

It is possible for an absolute value equation to have no solution.

Which of the following statements is not​ true?

It is possible for the distance between two points to be negative.

Let line 1 with slope m 1m1 and line 2 with slope m 2m2 be two nonvertical perpendicular lines. Which of the following statements is not ​true?

It is possible for the value of m 1m1 to be zero.